Thinking about the jetstream

These clouds at Dunwich Heath got me thinking. The lower level cumulus were visibly moving from left to right (that's south to north) but the higher level cirrus looked to be streaming towards me in the photograph - that's west to east. Could the cirrus be high enough to be in the jetstream? A plane flew over just above the level of the cirrus. I've looked up flights along that route which seems to be London to Scandinavia. One I found at this point was at 33000 ft. That's about 10000m. The jetstream does occur at that height.